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7th Grade Math / Lesson 4: Exponents

EXPONENTS
What will we be learning in this lesson?


  • This lesson will explain and demonstrate the use of exponents.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


EXPONENTS


Exponential form of a number looks like this: 4 3 which means 4*4*4

The 4 is the base: the number that gets multiplied repeatedly.

The 3 is the exponent or power: it tells how many times to multiply the base.

Ex) Exponential Form                         Factors*                 Standard form
         2 4                                           2 * 2 * 2 * 2                        16
         6 2                                               6 * 6                               36    

*factors: things that are multiplied together


EXPONENTS
 


EXPONENTS


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EXPONENTS


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EXPONENTS
Negative Exponents


  • Occasionally, there will be a negative exponent.

  • Negative exponents will result in a fractional value in standard form.

    Ex) 4 -2    becomes    1/42    which means 1/(4*4)    which equals 1/16

    Ex) 3 -1    becomes    1/31    which means 1/3         which equals 1/3


  • EXPONENTS


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    EXPONENTS


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    EXPONENTS
    Exponents that are Zero


    If your exponent is zero, the standard form of the number is 1. Raising a number to the power of zero means that you do not have any factors to multiply together.

    Ex) Exponential form          Standard form
                   5 0                                1
                 10 0                                1

    Any nonzero number raised to the zero power is 1.


    EXPONENTS
    Exponents that are Zero
     
    34    =  81
                Take one off of the exponent              Divide 81 by 3
    3 3   =  27
                Take one off of the exponent              Divide 27 by 3
    32     =   9
                Take one off of the exponent              Divide 9 by 3
    31    =   3
                 Take one off of the exponent             Divide 3 by 3
    3 0   =    1
                 Take one off of the exponent             Divide 1 by 3
    3 -1  =  1/3
                 Take one off of the exponent             Divide 1/3 by 3
    3-2   =  1/9